Related papers: Derived control theorems for reductive groups
We prove a Euler-Poincar\'e reduction theorem for stochastic processes taking values in a Lie group and we show examples of its application to SO(3) and to the group of diffeomorphisms.
We prove a version of Hilbert's Irreducibility Theorem in the quadratic case, giving a quantitative improvement to a result of Bilu-Gillibert in this restricted setting. As an application, we give improvements to several quantitative…
We develop aspects of geometric control theory on Lie groups G which may be infinite dimensional, and on smooth G-manifolds M modelled on locally convex spaces. As a tool, we discuss existence and uniqueness questions for differential…
We prove new quantitative bounds on the additive structure of sets obeying an $L^3$ 'control' assumption, which arises naturally in several questions within additive combinatorics. This has a number of applications - in particular we…
In this paper we stated a condition for the controllability of discrete-time linear systems for the case when the Lie group has finite semisimple center and provided a example in the Lie group $SL_2(\mathbb{R})$.
We characterize group compactifications of discrete groups for which there exists an equivariant retraction onto the boundary. In particular, we prove an equivariant analogue of Brouwer's No-Retraction theorem for large classes of group…
We introduce the notion of directed diagrammatic reducibility which is a relative version of diagrammatic reducibility. Directed diagrammatic reducibility has strong group theoretic and topological consequences. A multi-relator version of…
In this paper we explicitly calculate the control sets associated with a linear control system on the two dimensional solvable Lie group. We show that a linear control system of such kind admits exactly one control set or infinite control…
It is proved that the members of the Riccati hierarchy, the so-called Riccati chain equations, can be considered as particular cases of projective Riccati equations, which greatly simplifies the study of the Riccati hierarchy. This also…
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive…
The theory of controlled mechanical systems of [6, 3, 4] is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and…
In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched…
In this paper, we investigate the control sets of linear control systems on the Heisenberg group associated with singular derivations. Under the Lie algebra rank condition, we provide a complete characterization of these sets by analyzing…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
In this paper, a data-driven approach is developed for controller design for a class of discrete-time large-scale systems, where a large-scale system can be expressed in an equivalent data-driven form and the decentralized controllers can…
We study a sampled-data implementation of linear controllers that depend on the output and its derivatives. First, we consider an LTI system of relative degree $r\ge 2$ that can be stabilized using $r-1$ output derivatives. Then, we…
We define an unreduced version of the e-controlled lower $K$-theoretic groups of Ranicki and Yamasaki, and Quinn. We show that the reduced versions of our groups coincide (in the inverse limit and its first derived, $\lim^1$) with those of…
In this paper, we present conditions for the existence and uniqueness of chain control sets of discrete-time linear systems on the affine two-dimensional Lie group. More specifically, we prove that these chain control sets are given by the…
We present a method which allows reduction of a size of a simulated system. The method can be applied to any system where one can define a finite set of possible states of the system and an elementary process which transforms one state of…
In this paper, we investigate the analyticity of a class of exponential Dirichlet series. We then explicitly determine the coefficients of their power series decomposition and provide an estimate for the remainder. As an application, we…